Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems

Rudolf L. Voller

Applications of Mathematics (1992)

  • Volume: 37, Issue: 2, page 123-138
  • ISSN: 0862-7940

Abstract

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In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.

How to cite

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Voller, Rudolf L.. "Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems." Applications of Mathematics 37.2 (1992): 123-138. <http://eudml.org/doc/15704>.

@article{Voller1992,
abstract = {In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.},
author = {Voller, Rudolf L.},
journal = {Applications of Mathematics},
keywords = {partially ordered space; Newton-like iteration; affine-invariant; monotone including iteration methods; systems of nonlinear ordinary differential equations; partially ordered space; Newton-like iteration; affine-invariant; monotone including iteration methods; systems of nonlinear ordinary differential equations},
language = {eng},
number = {2},
pages = {123-138},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems},
url = {http://eudml.org/doc/15704},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Voller, Rudolf L.
TI - Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 2
SP - 123
EP - 138
AB - In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.
LA - eng
KW - partially ordered space; Newton-like iteration; affine-invariant; monotone including iteration methods; systems of nonlinear ordinary differential equations; partially ordered space; Newton-like iteration; affine-invariant; monotone including iteration methods; systems of nonlinear ordinary differential equations
UR - http://eudml.org/doc/15704
ER -

References

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  11. Schmidt J. W., Schneider H., 10.1007/BF02243015, Comput. 32 (1984), 1-11. (1984) MR0736257DOI10.1007/BF02243015
  12. Voller R. L., Monoton einschließende Newton-ähnliche Iterationsverfahren in halbgeordneten Räumen mit nicht notwendig regularem Kegel, Dissertation, Düsseldorf 1982. (1982) 
  13. Voller R. L., Iterative Einschließung von Lösungen nichtlinearer Differentialgleichungen durch Newton-ähnliche Iterationsverfahren, Apl. Mat. 31 (1986), 1-18. (1986) MR0836798
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